A Plan for Securing Observations of the Variable Stars

by Edward C. Pickering

V. Algol stars, or stars which for the greater portion of the time undergo no change in light, but every few days suffer a remarkable diminution in light for a few hours. This phenomenon recurs with such regularity that the interval between successive minima may be determined in some cases within a fraction of a second. Examples β Persei (Algol) and S Cancri.

Stars belonging to the first of these classes are seen so rarely that the apparent discovery of one is to be received with the utmost caution. On the other hand, the importance of early observations of such an object is so great that no pains should be spared to secure an early announcement if one is really found. On the best star charts many stars are omitted of the brightness of the faintest objects given. But any star much brighter than these should be measured by the method given below, and a watch kept to see if any change takes place. If it proves to be a temporary star an immediate announcement should be made. If a telegram is sent to this Observatory the object will be at once examined, and, if verified, notification will be made in this country and in Europe with the name of the discoverer or sender of the telegram. A similar notification may be sent of any suspected objects, which will be examined in the same way, and announced at once if they prove to be of interest. It is essential that the position of the object should be given with all the precision practicable, and that a letter should be sent by the next mail giving the observations in detail. This often proves of the greatest value in case the object is not readily found. It also serves to establish the claims of the first discoverer.

Nearly three quarters of the known variables belong to the second class. Most of them undergo very large changes of light, and may therefore be observed with comparative ease. Our knowledge of their variations is however very defective. Hitherto the attention of observers has been directed principally to determining the times at which they attain their maximum light, while their light at intermediate times has been neglected. It is now proposed to secure observations of these objects once or twice in every month, so that their light curves or variations throughout their entire periods may be determined. Again, many observers are accustomed to state their brightness in magnitudes without giving any clue to the scale which they employ. In most cases such observations have little value owing to the uncertainty of the scale of the fainter magnitudes.

According to Dr. Gould and some other observers most of the visible stars undergo slight changes of light and should therefore be assigned to the third class of variables. It is probable that our Sun also belongs to this class, as it is not likely that its light is the same during the maximum and minimum of the sun spot period. At present we are unable to tell in which case the light would be greatest. It by no means follows that when the spots are most abundant the Sun’s total light is least, for the remaining portions of the Sun may then have an increased brightness more than compensating for their diminished area. As long as the suspected variations in light of the stars are small, not exceeding half a magnitude for instance, they seem in the present state of science to have comparatively little interest. They are so liable to be affected, or even caused, by errors of observation, that the observation of such objects does not seem now to be advisable. Doubtless many such so-called variables are really due to errors caused by moonlight, the proximity of brighter stars, varying position of the images on the retina of the observer, and other similar causes. They will not therefore be considered further in this paper.

The stars of the fourth class as compared with the second are relatively few in number, and the changes in light small. While many of them need observation, especially to determine their light curves more precisely, it is advised that this work be left to those who have acquired a high degree of skill in these observations. That the work may be of value it is essential that the errors should be extremely small. As, however, nearly all are visible in an opera-glass, a skilful observer unprovided with a telescope may secure valuable results by their observation. This remark applies with especial force to many of those discovered in the southern heavens by Dr. Gould.

The phenomena of the Algol stars are in many respects the most striking of any. The rapidity of the changes, their surprising regularity, and the comparative rarity of these objects, combine to render the discovery of each new one a matter of unusual interest. As in the case of stars of the fourth class, however, the study of their light curves should be left to those who have acquired especial skill in this work. This is particularly desirable, when, as in this case, the unaided eye enters into competition with photometric apparatus, by which, as some think, it should properly be altogether replaced.

An elaborate bibliographical work on the variable stars has been undertaken at this Observatory by Mr. Chandler. It will include the collection of all available published observations of known or suspected variables. A catalogue of suspected variables has thus been prepared, doubtless containing many stars which are really important variables. But it is also likely that many objects have been introduced in the list by errors in the original observations. Such stars often appear in one catalogue after another of suspected variables, and it is difficult to prevent the continued circulation of such an error. Of course if an experienced observer at any time estimates a star as above or below its normal brightness, it is impossible to prove that the observation was not correct, and the star really variable. No amount of subsequent observing could prove that it had not then, and then only, an abnormal brightness. We can, however, prove that in all probability it does not belong to one or more of the above classes, and thus make it more and more probable that the observation is due to an error. If the star varies in light by one magnitude, what will be the chances that we shall get a series of observations having a range of variation of one fifth of a magnitude? Evidently on the average, there will be only one chance out of five that any observation shall fall in the same fifth of a magnitude as another. The chances for three such observations will be only 1/25 and for four 1/125, etc. These ratios expressed decimally are .2, .04, .008, 0016, .0003, etc. Since the separate determinations of the light of a constant star by the method given below should not differ more than two or three tenths of a magnitude, it is obvious that if the variations of the star are large, a few observations would generally establish this fact. If the star belongs to class four, observations on half a dozen evenings would hardly fail to show the variation. Conversely, if no such variation is detected we may be almost certain that the star is not a variable of that class, or at least that the variation, if any, is not large. If the star belongs to class two, it will change so slowly when near its maximum or minimum that a variation might not be noted if the observations are near together. An interval of several months should therefore be allowed to take place, or perhaps it would be better to wait until the star is again visible the following year. The total variation in light is usually so great in these stars that the change will often be visible at the first glance.

To prove that a star does not belong to the fifth class is a matter of much greater difficulty. In fact it is almost impossible to prove that it may not be an Algol star with a long period between the minima. Since these stars may have their full brightness for nine tenths of the time, it is obvious that they may be examined again and again without happening to be seen at the time of a minimum.

On the other hand, during a considerable portion of the time when it is varying, the light will be so much less than usual that a careful measurement is not needed to detect the change. Moreover, it will be useless to look for an increase of light, and the observation may be so planned as to detect a diminution only.

If we assume that only during one tenth of the time the change in light will be sufficient to be perceptible, the chance on any given evening will be 9 out of 10 or 9/10 that the star will have its full brightness. For two evenings the chance will be (9/10)² for three (9/10)³, etc. These quantities expressed decimally are .9, .81, .73, .66, .59, .53, .48, etc. Even after seven nights’ observations, on which no change is noted, it will only be about an even chance that the star may not still be of the Algol type. A different method of observing is therefore recommended when the star is supposed to belong to this class. Select for comparison a star slightly fainter, so that a moment’s glance will satisfy the observer that the suspected variable is the brighter. It is only necessary to repeat this observation night after night. If the star is bright enough to be visible with a field glass, a few seconds will be sufficient for this observation after the observer has become familiar with the vicinity. The fact that the light is normal, and the time to the nearest minute, should be recorded after each observation. When convenient, it is well to repeat the inspection two or more times during the night, as in determining the period all the observations will have a value, provided that they are separated by intervals of more than two or three hours. If the star is ever found below its normal brightness, comparisons should be made with the adjacent stars, and continued as long as possible, or until it has regained its usual brightness. The most complete proof that a star was not of the Algol type would be for observers in the polar regions to examine it at intervals of a few hours for several days, or for observers in different longitudes to make the same observations. If it could thus be watched for a week or fortnight by enough observers to avoid interference by clouds, it would be nearly certain that it is not an Algol star unless its period is greater than that of any such object as yet discovered.